Developing R software for simultaneous estimation of Q- and R-mode Factor Analyses using spatial and non spatial data

Abstract

Simultaneous use of R- and Q-mode Factor Analysis is a powerful similarity measurement among and between variables and objects of a continuous data, but its availability is lacking in R statistical software environment. I have developed a new R package called qrfactor that can perform Factor Analysis on spatial and non spatial data. The package contains one function called qrfactor() that can perform various versions of Factor Analyses such as PCA, R-mode Factor Analysis, Q-mode Factor Analysis, Simultaneous R- and Q-mode Factor Analysis, Principal Coordinate Analysis, as wells as Multidimensional Scaling (MDS) and cluster analysis. The qrfactor() function returns values such as eigenvalues, eigenvectors, loadings, scores, and indices. Unlike other R package factor analysis functions, plot.qrfactor() offers several annotated biplots for all possible combinations of eigenvectors, loadings, and scores as well as the possibility of plotting about 60 maps in gray and full colour scales. The empirical and Eckhart–Young theorem evaluations show that ‘qrfactor’ package is mathematically correct in estimation of simultaneous R-and Q-mode Factor Analysis. The results are also in agreement with the results of other classical statistical functions and packages. Using one function to estimate various dimensions of factor analyses reduces the learning curve in R environment.

Keywords: GIS, qrfactor, loadings, Multi-dimensional, R package, Factor scores, Cluster Analysis, Eckhart–Young, maps